In Refs. [1]}, [2]}, [3]}, [4]},
the method by the hopping parameter expansion was adopted to investigate the critical point of QCD with heavy quarks on \(N_t=4\)  and 6 lattices, where \(N_t\)  is the temporal extent of the lattice.
This method was extended to finite densities in Refs. [5]}, [2]}.
In Refs. [2]}, [3]}, an effective method was proposed to incorporate the next-to-leading order effect of bent Polyakov loops by a shift of the coefficient for the leading-order Polyakov loop term, and the truncation error was estimated from the difference between the leading-order and the next-to-leading order calculations.
In Ref. [4]}, a finite size scaling analysis was adopted to obtain the critical point in the thermodynamic limit, where, to overcome the overlapping problem on spatially large lattices, the configurations are generated by an action incorporating the leading-order effect by the Polyakov loop term, and the next-to-leading order effect is taken into account by the reweighting.
The hopping parameter expansion was applied also to QCD with mixed heavy and light quarks [5]}, [11]}.
